Answer:
answer below
Step-by-step explanation:
9(y = 1/9x + 5)
9y = x + 45
-x + 9y = 45
x - 9y = -45
2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^2at
Hint: Turn tan(x) = e^at and e^y = 1 + e^2at into expressions suited to your calculation.
I assume a is a constant. If tan(x) = exp(at) (where exp(x) means eˣ), then differentiating both sides with respect to t gives
sec²(x) dx/dt = a exp(at)
Recall that
sec²(x) = 1 + tan²(x)
Then we have
(1 + tan²(x)) dx/dt = a exp(at)
(1 + exp(2at)) dx/dt = a exp(at)
dx/dt = a exp(at) / (1 + exp(2at))
If exp(y) = 1 + exp(2at), then differentiating with respect to t yields
exp(y) dy/dt = 2a exp(2at)
(1 + exp(2at)) dy/dt = 2a exp(2at)
dy/dt = 2a exp(2at) / (1 + exp(2at))
By the chain rule,
dy/dx = dy/dt • dt/dx = (dy/dt) / (dx/dt)
Then the first derivative is
dy/dx = (2a exp(2at) / (1 + exp(2at))) / (a exp(at) / (1 + exp(2at))
dy/dx = (2a exp(2at)) / (a exp(at))
dy/dx = 2 exp(at)
Since dy/dx is a function of t, if we differentiate dy/dx with respect to x, we have to use the chain rule again. Suppose we write
dy/dx = f(t)
By the chain rule, the derivative is
d²y/dx² = df/dx
d²y/dx² = df/dt • dt/dx
d²y/dx² = (df/dt) / (dx/dt)
d²y/dx² = 2a exp(at) / (a exp(at) / (1 + exp(2at)))
d²y/dx² = 2 (1 + exp(2at))
Austin is running. The number of calories he has burned varies directly with the number of minutes he has run. See the graph below. 400 350+ 300 250 + Calories burned 200+ 150 100+ 50+ 0 20 10 30 80 Number of minutes
a) how many minutes does austin run per calories burned?
b) what is the slope of the graph?
Answer:
223454353.000000000000000000
Step-by-step explanation:
A refrigeration system of 60 kW capacity at an evaporator temperature of – 40°C and a condenser temperature of 20°C is needed in a food storage locker. The refrigerant R134a is sub-cooled by 10°C before entering the expansion valve. The vapour is 0.98 dry as it leaves the evaporator coil. The compression in the compressor is of adiabatic type.
what is the equation for: 32 is the sum of a number x and 9
Answer:
x + 9 = 32
Step-by-step explanation:
answer for x is 32 - 9 = 23
Which number comes next in the series? 7, 10, 10, 13, 16, 16,
Answer:
19
Step-by-step explanation:
In the first number, they add three and that number is repeated.
To further explain, the series would continue like this:
7, 10, 10, 13, 16, 16, 19, 22, 22...
Hope this helps! Brainliest would be appreciated!
What is the eighth term of the arithmetic sequence defined by the rule A(n) = -12 + 2(n-1)?
Tn = a + d * (n-1)
T8 = -12 + 2*7
= -12 +14
= 2
What are the odds of choosing a blue marble from a bag that contains two blue marbles, one green marble and four red marbles?
Answer:
1/3
Step-by-step explanation:
2 blue 1 green 4 red
Grandma Maude wanted a tall cake for her 80th birthday. The baker made a cake with 4x3 – x layers. Each layer was 2 + 3x2 cm. Which expression shows the total height of Grandma Maude’s cake?
Using proportions, it is found that the expression that shows the total height of Grandma Maude’s cake is:
[tex]t = 12x^5 + 5x^3 - 2x[/tex]
This question is solved by proportions, using a rule of three.The measure of one layer, in cm, was of [tex]2 + 3x^2[/tex]. In total, there were [tex]4x^3 - x[/tex] layers.The rule of three is:
1 layer - [tex]2 + 3x^2[/tex] cm
[tex]4x^3 - x[/tex] layers - t cm
Applying cross multiplication:
[tex]t = (4x^3 - x)(2 + 3x^2) = 12x^5 + 5x^3 - 2x[/tex]
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
Answer:
12x5 + 5x3 – 2x cm
Step-by-step explanation:
What is 1.8 added 8 times? (IF YOU CAN PLS DO IT IN EXPLANATION) and this is about decimals and pls do it in grade five type, bc I won't be able to understand anything too big for me, example: (e^(4^(2)
Thank you
Answer:
14.4
Step-by-step explanation:
1.8 added 8 times = 1.8 * 8
1.8 * 8
use distributive property
1.8 = 1 + 0.8
1.8 * 8 = (1+0.8) * 8
= 1*8 + 0.8*8
anything multiplied by 1 equals itself
1*8 + 0.8*8 = 8 + 0.8 * 8
0.8 = 8/10
0.8 * 8 = (8/10) * 8
= 64/10
= 6.4
8 + 0.8 * 8 = 8 + 6.4 = 14.4 as our answer
4. This diagram is a straightedge and compass construction of a line perpendicular to line AB passing through point C. Which segment has the same length as segment EA.
a. EC
b. ED
C. BE
d. BD
Answer:
Segment ED has the same length as EA
The line segment which is equal to EA is ED. Therefore, option B is the correct answer.
In the given diagram, a line perpendicular to line AB passes through point C.
What is the tangent to the circle?A tangent to a circle is a line which intersects the circle at only one point. The common point between the tangent and the circle is called the point of contact.
The length of two tangents drawn from an external point to a circle is equal.
From the given figure we can see there are three circles, two large circles and one small circle.
Line segment EA is tangent to a small circle.
The line segment which is equal to EA is ED because ED is another tangent to a small circle from the same external point.
The line segment which is equal to EA is ED. Therefore, option B is the correct answer.
To learn more about the tangent to a circle visit:
https://brainly.com/question/16592747.
#SPJ2
To make cupcakes Leah uses 1/2 cup of chocolate chips for evry 1 1/3 cups of batter if Leah uses 3/4 cups of chocolate chips how many cups of batter should she use
Answer:
2
Step-by-step explanation:
Leah uses 1/4 cup of chocolate chips for 2/3 cups of batter, so if Leah uses 3/4 cup of chocolate chips, she should use 2 cups of batter.
End of semester geometry Semester A question 6
Select the correct answer.
Given:
Prove:
By the linear pair theorem, is supplementary to . Since , by the definition of congruence, . Applying the substitution property of equality, . Simplifying the equation, .
What step is missing from this proof?
A.
is supplementary to by the transitive property.
B.
by the definition of supplementary angles.
C.
by the definition of congruence.
D.
by the linear pair theorem.
Answer:
by the definition of congruence.
Step-by-step explanation:
for plato
the two windows shown are similar. What is the height of the larger window?
Answer:
The height of the larger window is 15.36 units.
Step-by-step explanation:
Let the height of the larger window be h.
The width and height of smaller window are 5 and 8 respectively.
The width and height of smaller window are 9.6 and h respectively.
It is given that both windows are similar. The corresponding sides of similar figures are proportional.
\frac{5}{9.6}=\frac{8}{h}
9.6
5
=
h
8
5h=8\times 9.65h=8×9.6
5h=76.85h=76.8
Divide both sides by 5.
h=\frac{76.8}{5}=15.36h=
5
76.8
=15.36
Therefore the height of the larger window is 15.36 units.
y=5/9x+9, find the slope
need help with this problem
Check the picture below.
Which statement is the correct interpretation of the inequality −4 > −5? (5 points)
Question 7 options:
1)
On a number line, −4 is located to the left of 0 and −5 is located to the right of 0.
2)
On a number line, −4 is located to the right of 0 and −5 is located to the left of 0.
3)
On a number line, −4 is located to the right of −5.
4)
On a number line, −4 is located to the left of −5.
Answer:
On a number line, -4 is located to the right of -5
Step-by-step explanation:
Answer:
On a number line, -4 is located to the right of -5.
Step-by-step explanation:
this is correct, also I don't take credit for it the person above me is the original. :)
what is the perimeter of a rectangular whose area is 92 square mm and length is 11.5 mm
We are given –
Area of rectangular is = 92 square mmLength of rectangular is = 11.5 mmWe are asked to find out the value of perimeter of the rectangular! Let's find it's breadth first!We know that–
[tex]\qquad[/tex][tex] \purple{\bf\longrightarrow Area_{(Rectangular)} = Length \times Breadth} [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 92 = 11.5 \times Breadth [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Breadth = \cancel{\dfrac{92}{11.5}}[/tex]
[tex]\qquad[/tex][tex] \purple{\bf \longrightarrow Breadth = 8 \: mm}[/tex]
Now, Perimeter of rectangular –
[tex]\qquad[/tex][tex] \pink{\bf \longrightarrow Perimeter _{(Rectangular) } = 2( Length + Breadth) }[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Perimeter _{(Rectangular) }= 2( 11.5 +8) [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Perimeter _{(Rectangular) } = 2 \times 19.5[/tex]
[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow Perimeter _{(Rectangular) } = 39\: mm}[/tex]
Henceforth, Perimeter of rectangular is 39mm._______________________________________
Answer:
Perimeter = 39 mmStep-by-step explanation:
In this question we are given with ,
Area of rectangle = 92 sq mmLength of rectangle = 11.5 mmAnd we're asked to find the perimeter of rectangle .
Solution : -
We know that ,
[tex] \pink{ \boxed{\sf{Area \: of \: rectangle = L × W}}}[/tex]
Where ,
L = length of rectangleW = width of rectangleSo from this formula we can find the width of rectangle and equating it with 92 ( because 92 is the given area ) . Substituting value of length :
[tex] \longmapsto \: 11.5 \times W = 92[/tex]
Step 1 : Multiplying 11.5 and W :
[tex] \longmapsto \: 11.5W = 92[/tex]
Step 2 : Dividing by 11.5 on both side :
[tex] \longmapsto \: \frac{ \cancel{11.5}W}{ \cancel{ 11.5}} = \frac{92}{11.5} [/tex]
On further calculations we get :
[tex] \longmapsto \: W = \cancel{\frac{920}{115} }[/tex]
Step 3 : By cancelling 920 by 115 we get :
[tex] \longmapsto \: \purple{\boxed{ \bold{W = 8 \: mm}}}[/tex]
Therefore , width of rectangle is 8 mm .Finding Perimeter :We know that ,
[tex] \blue{ \boxed{ \sf{Perimeter \: of \: rectangle = 2 ( L +W )}}}[/tex]
Where ,
L = Length of rectangle W = Width of rectangleSubstituting values in formula :
[tex] \longrightarrow \: 2(11.5 + 8)[/tex]
Step 1 : Solving parenthesis :
[tex] \longrightarrow \: 2(19.5)[/tex]
Step 2 : Multiplying 2 with 19.5 :
[tex] \longrightarrow \: \green{\boxed{ \bold{39 \: mm}}}[/tex]
Therefore, perimeter of rectangle is 39 mm. #Keep LearningIn solving the following system of equations, how many equations do you need to multiply in order to use the method of elimination?
Equation 1: −5x−20y=−15 Equation 2: 2x + 8y = 6
A. Two
B. None
C. One
Give the solution to the system above
A. No solution
B. (3, 7)
C. IMS
D. ( -2, 5)
Answer:
a and d i think
Step-by-step explanation:
PLEASE HELP THIS WILL GIVE 50 POINT AND BRAINLIEST！！！！！!
In introductory physics, a typical cavendish balance for measuring the gravitational constant G use metal masses 2.39kg and 16g whose center are separated by 6.81cm calculate the gravitation force between these forces, treating each as a point mass located at the center of the sphere.
gravitational constant =6.67259 × 10⁻¹¹N·m²/kg²
Answer:
the asnswer is -67463 to the power of 4
Step-by-step explanation:
A 20 cm long thin wire is used to form a square. What is the area of the square?
Answer:
25cm^2
Step-by-step explanation:
A square has 4 equal sides so each side will be 20/4 = 5cm
Easily calculate the area by taking 5 x 5 = 25cm^2
someone please help me giving brainlist
Answer:
A
Step-by-step explanation:
A house costs 36% more today than when it was built.If the cost of the house today is $333,200, find the cost when it was built.
Answer:
$245,000
Step-by-step explanation:
Let the intial cost = x
[tex]100\% + 36\% = 136\% = 1.36[/tex]
[tex]1.36x = 333200[/tex]
[tex]x = \frac{333200}{1.36} [/tex]
[tex]x = 245000[/tex]
Pls help with these questions!
Answer:
I don't know sorry
A group of pigs and ducks has a total of 40 feet. There are twice as many ducks as pigs. How many of each animal are there?
The question relates to the total number of pairs of feet ducks and a pigs
are known to have.
There are 5 pigs and 10 ducksReasons:
The length of the group of ducks and pigs = 40 feet
Number of ducks = Twice the number of pigs
Each duck has 2 feet.Each pig has 4 feet.Let x represent the number of pigs, and let y represent the number of ducks, we have;
y = 2 × x
4·x + 2·y = 40
Which gives;
4·x + 2 × (2·x) = 40
8·x = 40
x = 40 ÷ 8 = 5
The number of pigs, x = 5y = 2 × x
Therefore;
y = 2 × 5 = 10
The number of ducks, y = 10Learn more about solving word problems in mathematics here:
https://brainly.com/question/25272317
which relation is a function? PLEASE HELPPPPP
Step-by-step explanation:
in the first
x =2y
actually I don't think that I can get the last two relations
Which number line represents the number 0.7
Answer:
What number like?
Answer: The answer is C.
The question I assume you are talking about is in the image.
What is 50 million + 32 hundred thousands + 41 hundred
Answer:
82041000
Step-by-step explanation:
50,000,000 + 32,000,000 + 41,000
100 POINTS WILL AWARD BRAINLIEST PLEASE HELP
(IMAGE INCLUDED)
In the image below, the m
Answer: 67°.
Step-by-step explanation:
1) m∠PMR=m∠LMN=3x+19°;
2) m∠LMN+m∠LMP=180°, it can be written as 3x+19+9x-31=180;
3) if to solve the equation 3x+19+9x-31=180, then x=16;
4) m∠PMR=3x+19=48+19=67°.
Find x
Linear pairs are supplementary
9x-31+3x+19=18012x-12=180x-1=15x=15+1=16So
opposite angles are equal
m=9(16)-31=144-31=113°Complete the table of ordered pairs for the linear equation
Answer:
Step-by-step explanation:
See attachment.
What is the answer to the following question?
Answer:
SAS similarity
Step-by-step explanation:
You have two side ratios and the angle between the sides with those ratios. The appropriate similarity theorem is SAS.
If [tex]a + ar + ar^{2} + ... = 15[/tex] and [tex]a + ar^{2} + ar^{4} + ar^{6} + ... = 9[/tex], then what is the sum of the geometric series [tex]a + ar^{3} + ar^{6} + ar^{9} + ...[/tex]?
Notice that
a + ar³ + ar⁶ + ar⁹ + ... = a + r³ (a + ar³ + ar⁶ + ...)
but the grouped sum on the right side is the same as the sum on the left side. This means that, if the sum we want to compute
a + ar³ + ar⁶ + ar⁹ + ...
converges to S, then
S = a + r³ S
Solve for S :
S - r³ S = a
(1 - r³) S = a
S = a/(1 - r³)
Similarly, knowing the value of the first sum, we have
a + ar + ar² + ar³ + ... = a + r (a + ar + ar² + ...)
but we know
a + ar + ar² + ... = 15
so
15 = a + 15r
and knowing the value of the second sum, we have
a + ar² + ar⁴ + ... = a + r² (a + ar² + ar⁴ + ...)
so
9 = a + 9r²
Solve these two equations for a and r :
15 = a + 15r ⇒ a = 15 - 15r
9 = a + 9r² ⇒ 9 = 15 - 15r + 9r² ⇒ 3r² - 5r + 2 = (3r - 2) (r - 1) = 0
⇒ r = 2/3 or r = 1
We cannot have r = 1, since that would mean
a + a + a + ... = 15
since the left side is adding infinitely many copies of some constant; such a sum can never converge to a finite number. So it must be that r = 2/3, and it follows that a = 15 - 15 (2/3) = 5.
Then the sum we want has a value of
S = 5/(1 - (2/3))³ = 135/19
Answer:
Step-by-step explanation:
a + ar¹ + ar² + ar³ + ... = 15 #1
r(a + ar¹ + ar² + ar³ + ...) = 15r
ar¹ + ar² + ar³ + ... = 15r #2
subtract #2 from #1
a = 15 - 15r
a + ar² + ar⁴ + ar⁶ + ... = 9 #3
r²(a + ar² + ar⁴ + ar⁶ + ... )= 9r²
ar² + ar⁴ + ar⁶ + ... = 9r² #4
subtract #4 from #3
a = 9 - 9r²
15 - 15r = 9 - 9r²
9r² - 15r + 6 = 0
3r² - 5r + 2 = 0
r = (5 ±√(5² - 4(3)(2))) / (2(3)
r = (5 ± 1) / 6
r = 1
or
r = 4/6 = 2/3
if r = 1 then a = 15 - 15(1) = 0 and a series of zeros added together can never equal 15 so r = 2/3 must be true.
a = 15 - 15(2/3) = 5
a + ar³ + ar⁶ + ar⁹ + ... = C #5
r³(a + ar³ + ar⁶ + ar⁹ + ...) = Cr³
ar³ + ar⁶ + ar⁹ + ... = Cr³ #6
subtract #6 from #5
a = C - Cr³
a = C(1 - r³)
C = a/(1 - r³)
C = 5/(1 - (2/3)³)
C = 5/(1 - 8/27)
C = 5/(19/27)
C = 5(27/19)
C = 135/19 = 7.1052631578947368....